The instructions given by J.A. Dahlgren in the early U.S. Navy boat howitzer manuals, call for ammunition boxes to be slung under and lashed to the axle bed of the iron field carriage.
System Of Boat Armament In The United States Navy: Reported To Commodore Charles Morris, Chief Of Bureau Of Ordnance And Hydrography. By J.A. DAHLGREN Assistant Inspector Of Ordnance (In Charge Of Experimental Department.) Philadelphia: Printed By A. Hart, 126 Chestnut Street. 1852, P. 27.
Dahlgren Boat HowitzerPhoto by Andrew Trehubenko taken at the Maritime Industry Museum, Fort Schuyler, the Bronx, NY
This U.S. Navy instruction book published in 1860 still has the boxes lashed under the axle, but it also relates some interesting information about securing two field carriages together, and carrying the ammunition boxes on spars attached above the axles.
Ordnance instructions for the United States Navy, U.S. Navy Dept. Bureau of Ordnance, John Adolphus Bernard Dahlgren, Navy Dept, Washington: George W. Bowman, Public Printer, 1860: see p. 109
http://books.google.com/books?id=OEhUZmgQ4GIC&dq=John%20A.%20Dahlgren%20book%20on%20Boat%20Howitzers&lr=&pg=PA109&output=text"NOTES ON THE USE OF BOAT HOWITZERS. 109
356. Field Carriage.—In order to moderate the recoil on smooth ground, take out the axle or pin of the trail wheel and turn the wheel up on the trail.
In using the howitzer on shore one or two double boxes of ammunition may be lashed under the axle of the field carriage. When more than a single piece is landed it may be found convenient to secure the trail of one field carriage to the axle of another, and then, by means of pieces of stuff, or boat's spars, secured from axle to axle, to place the ammunition boxes, provisions, pouches, &c., upon them. "
Page 144 of this book shows a table that gives the same measurements of the ammunition boxes as the table that navygunner posted (viewed from the top these ammo boxes would be almost square).
Drawing showing the boxes stacked and lashed on spars resting upon the axles, with the implements stored in the bores.
Instruction For Naval Light Artillery, Afloat And Ashore. Prepared And Arranged For The U.S. Naval Academy, By William H. Parker, Lieut. U.S.N., Second Edition, Revised By Lieut. S. B. Luce, U.S.N., New York: D. Van Nostrand, 192 Broadway. 1863. See p. 14
http://www.archive.org/stream/cu31924030896942#page/n0/mode/1upPage 14:
"Two boxes of ammunition will be carried on top of the axle-tree, and each man, with the exception of Nos. 1 and 3, will carry one round in his pouch." I don't know the exact timeline of when this boat howitzer field carriage improvement came about, but at least by 1863 a rack was designed to be mounted above the axle-tree on the carriage, and it would hold the ammunition chest with two upright pins that fit into the bottom of the chest.
Photo is from the Civil War website "To the Sound of the Guns", markerhunter.wordpress.com
A Text-Book Of Naval Ordnance And Gunnery. Prepared For The Use Of The Cadet Midshipmen At The United States Naval Academy. By A. P. Cooke, Commander, U.S.N. Second Edition Revised And Enlarged. Volume II. New York: John Wiley & Sons 15 Astor Place. 1880. See pp. 391-392, and Fig. 255 on p. 392 (a drawing of a Dahlgren boat howitzer on a field carriage carrying two ammunition chests).
http://www.archive.org/details/textbookofnavalo02cookuoft"The Field-carriage ashore. — As it is designed to operate independently of a limber, light composition frames, having pins projecting upward, are attached to the trail and axle on each side, on which the ammunition-boxes rest. Their bottoms are fitted with metal sockets for the projecting pins of the frames."Edit: Changed the publication date on the first book listed (System Of Boat Armament In The United States Navy) from 1856 to 1852, and added a link.